PSI - Issue 59

Victor Aulin et al. / Procedia Structural Integrity 59 (2024) 444–451 Victor Aulin et al. / Structural Integrity Procedia 00 (2019) 000 – 000 3

446

where ( ) f S – is the function of activation. The layers of a neural network can be conditionally divided into three groups:

– the first layer of neurons in a multilayer neural network serves as the input layer and consists of neurons that are responsible for receiving data (signals) and further transmitting them to the inputs of the hidden layer of the neural network; – hidden (intermediate) layers of neurons are crucial because they often make up the majority of the neural network's structure, where computations are performed using activation function formulas; – the output layer represents the result of the neural network's operation. The choice of the activation function (sigmoid) is determined by its differentiability along the entire abscissa axis and its very simple derivative (Dia 2001; Król 2016). When using the error (defect) backward propagation algorithm, this facilitates the acceleration of the training process of the neural network method. The output value of a neuron with a sigmoid activation function takes the following form: 1 )) ( ) (1 exp(      S Y f S  , (3) The content of signals and their corresponding coefficients of specific weight is provided to the summation block. Schematic representation of an artificial neuron model is shown on fig.1.

x 1 x 2 x 3

w 1 w 2 w 3 ... w n

Y = f ( S ) - activation function of efficiency

Signal summation block

S

Y

...

x j

Fig.1. Schematic representation of an artificial neuron model.

1 2 ( , ,..., ) j X x x x 

The number of input signals is denoted by vector j x x x , ,..., 1 2 have their own coefficients of specific weight n w onthespecifiedinputs, which represent the strength of the synaptic connection. Their set is denoted by the vector of specific weight 1 2 ( , ,..., ) n W w w w  . As a result of summation, the obtained value serves as an argument for the activation function, which then generates the output value Y. The production losses  C associated with the provision of maintenance and repair operations complex and errors in distributing defects in components, systems, and assemblies can be expressed as a functional: , where

) ( ij ij C f C P   ,

(4)

where ij C – are the summarized losses as so ciated with the provision of maintenance and repair operations complexofunits, systems, and assemblies aimed at detecting andr emovin ga i - defect of a j -unit, systemor assembly, related to the maintenance and repair complex of operations; ij P – is probability of an eventdealing withthe recognition error of i -defectofa j -unit, systemor assembly, that is serviced or repaired:

  ,

(5)

ij P

 

ij

ij